what is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83

Answer:The 17th term in arithmetic sequence is 68Step-by-step explanation:The general formula of arithmetic sequence is:aₙ = a₁ + (n – 1)d.We are given a₆ = 101 and a₉ = 83 and we need to find a₁₇To find the term a₁₇ we should know a₁ and d. So we would find botha₆ = a₁ +(6-1)d101 = a₁ +(5)d101 = a₁ +5d     eq(1)and a₉ = a₁ +(9-1)d     83 = a₁ + 8d       eq(2)Subtracting eq(2) from eq(1)101 = a₁ +5d83 = a₁ + 8d -       -     -__________18 = -3d=> d = 18/-3=> d = -6Putting value of d in eq(1)101 = a₁ + 5d101 = a₁ + 5(-3)101 = a₁ -15=> a₁ = 101+15=> a₁ = 116Now finding a₁₇:aₙ = a₁ + (n – 1)d.a₁₇ = 116 +(17-1)(-3)a₁₇ = 116+(16)(-3)a₁₇ = 116 - 48a₁₇ = 68So, the 17th term in arithmetic sequence is 68